Leicester won seven of their last nine fixtures during the 2014-15 campaign to remain in the league and Sunderland survived last year by avoiding defeat in their last six games.
"You can get improbable results and late rallies at this time of the year," Agnew told British media.
"It's happened in recent seasons with both Sunderland and Leicester. They have shown that one win can literally change lots of things and it can also affect other teams around you in the table, so that's what we aim to do."
Middlesbrough will be aiming for their fourth home league win of the season when they host Arsenal on Monday.
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(Reporting by Aditi Prakash in Bengaluru, editing by Pritha Sarkar)
